Steric 6 cubes

Updated on Nov 27, 2024

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In six-dimensional geometry, a steric 6-cube is a convex uniform 6-polytope. There are unique 4 steric forms of the 6-cube.

Alternate names

Runcinated demihexeract/6-demicube

Small prismated hemihexeract (Acronym sophax) (Jonathan Bowers)

The Cartesian coordinates for the 480 vertices of a steric 6-cube centered at the origin are coordinate permutations:

(±1,±1,±1,±1,±1,±3)

with an odd number of plus signs.

Runcitruncated demihexeract/6-demicube

Prismatotruncated hemihexeract (Acronym pithax) (Jonathan Bowers)

The Cartesian coordinates for the 2880 vertices of a stericantic 6-cube centered at the origin are coordinate permutations:

(±1,±1,±1,±3,±3,±5)

with an odd number of plus signs.

Runcicantellated demihexeract/6-demicube

Prismatorhombated hemihexeract (Acronym prohax) (Jonathan Bowers)

The Cartesian coordinates for the 1920 vertices of a steriruncic 6-cube centered at the origin are coordinate permutations:

(±1,±1,±1,±1,±3,±5)

with an odd number of plus signs.

Runcicantitruncated demihexeract/6-demicube

Great prismated hemihexeract (Acronym gophax) (Jonathan Bowers)

The Cartesian coordinates for the 5760 vertices of a steriruncicantic 6-cube centered at the origin are coordinate permutations:

(±1,±1,±1,±3,±5,±7)

with an odd number of plus signs.

There are 47 uniform polytopes with D₆ symmetry, 31 are shared by the B₆ symmetry, and 16 are unique:

(Text) CC BY-SA